Question

1. (19 pts) Adrienne and Deepa consume pizza, Z, and cola, C. Adrienne's utility function is UA = ZĄCA and Deepa' s utility function is U = 295c9S. Adrienne' s marginal utility of pizza is MUZ = CA, and her marginal utility of cola is MUS = ZA. Similarly, Deepa' s marginal utility of pizza is MU] =2,05095 and her marginal utility of cola is MUY =2,5c, 0.5. Their initial holdings of pizza and cola are 2A = 10, CA = 20, 2p = 20,Cp = 10. a) (4 pts) Draw an Edgeworth box for Adrienne and Deepa with width of the box representing quantity of pizza and height of the box representing quantity of cola. Place Adrienne's origin at the lower left corner and Deepa's origin at the upper right corner. Determine the height and width of the Edgeworth box. b) (5 pts) Indicate the initial holdings of pizza and cola in your Edgeworth box. Is the initial allocation of pizza and cola pareto-efficient? Explain. Sketch the consumers' indifference curves that go through the initial allocation. c) (5 pts) Consider a new allocation of the two goods: 2A = 18,CA = 18, Zp = 12, C, = 12. Is this allocation pareto-efficient? Explain. Sketch the consumers' indifference curves that go through this allocation. d) (5 pts) What is the formula for the contract curve? Indicate the contract curve in your Edgeworth box.

Answer 1

UA - ZACA ZA = 10 . CA = 20 Vo = 2,05 COS ZD = 20 Co -10 20120) C 301 height = 30 cola. Width - 30 Pizza. CA zot to VA CA 172505605 Point f shows the initial holding by AfD. for paret optimality MARSEJARE_MRSA - MRSD ZA Y 2015 6605 LA - at initial endowment 20 & 10 , so jnitial endocoment is not pareto efficient. ----- c) ZA = 10 Zp =12 CA = 18 Co =12 the above allocation is pereeto efficient as MRSA = MRS, the 42 → 1=1 C 3o VA contece Contract care 18 + -- d) Contract were is CARE (clculeted yn b) ON